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Question: Scalar function in metric - DifferentialGeometry

Question:Scalar function in metric - DifferentialGeometry

Michael_Watson 125 Maple 18
December 15 2014
2

I am using Maple 18 on a Mac. I also uploaded the tetrad package.  I setup my metric but when I call Christoffel I get the following error.

 

> 

restart; with(DifferentialGeometry); with(Tensor); with(Tools)
> 

DGsetup([zeta, zetabar, u, v], M1, verbose);

`The following coordinates have been protected:`

  

[zeta, zetabar, u, v]

  

`The following vector fields have been defined and protected:`

  

[_DG([["vector", M1, []], [[[1], 1]]]), _DG([["vector", M1, []], [[[2], 1]]]), _DG([["vector", M1, []], [[[3], 1]]]), _DG([["vector", M1, []], [[[4], 1]]])]

  

`The following differential 1-forms have been defined and protected:`

  

[_DG([["form", M1, 1], [[[1], 1]]]), _DG([["form", M1, 1], [[[2], 1]]]), _DG([["form", M1, 1], [[[3], 1]]]), _DG([["form", M1, 1], [[[4], 1]]])]

  

`frame name: M1`

 (1)
M1 > 

g := evalDG(2*`&t`(dzeta, dzetabar)+2*`&t`(du, dv)+2*H(zeta, u, v)*`&t`(du+Y(zeta, u, v)*dzetabar+Ybar(zeta, u, v)*dzeta-Y(zeta, u, v)*Ybar(zeta, u, v)*dv, du+Y(zeta, u, v)*dzetabar+Ybar(zeta, u, v)*dzeta-Y(zeta, u, v)*Ybar(zeta, u, v)*dv));

_DG([["tensor", M1, [["cov_bas", "cov_bas"], []]], [[[1, 1], 2*H(zeta, u, v)*Ybar(zeta, u, v)^2], [[1, 2], 2*H(zeta, u, v)*Y(zeta, u, v)*Ybar(zeta, u, v)+2], [[1, 3], 2*H(zeta, u, v)*Ybar(zeta, u, v)], [[1, 4], -2*H(zeta, u, v)*Ybar(zeta, u, v)^2*Y(zeta, u, v)], [[2, 1], 2*H(zeta, u, v)*Y(zeta, u, v)*Ybar(zeta, u, v)], [[2, 2], 2*H(zeta, u, v)*Y(zeta, u, v)^2], [[2, 3], 2*H(zeta, u, v)*Y(zeta, u, v)], [[2, 4], -2*H(zeta, u, v)*Y(zeta, u, v)^2*Ybar(zeta, u, v)], [[3, 1], 2*H(zeta, u, v)*Ybar(zeta, u, v)], [[3, 2], 2*H(zeta, u, v)*Y(zeta, u, v)], [[3, 3], 2*H(zeta, u, v)], [[3, 4], -2*H(zeta, u, v)*Y(zeta, u, v)*Ybar(zeta, u, v)+2], [[4, 1], -2*H(zeta, u, v)*Ybar(zeta, u, v)^2*Y(zeta, u, v)], [[4, 2], -2*H(zeta, u, v)*Y(zeta, u, v)^2*Ybar(zeta, u, v)], [[4, 3], -2*H(zeta, u, v)*Y(zeta, u, v)*Ybar(zeta, u, v)], [[4, 4], 2*H(zeta, u, v)*Y(zeta, u, v)^2*Ybar(zeta, u, v)^2]]])

 (2)
M1 > 

R1 := Christoffel(g, "FirstKind")

Error, (in DifferentialGeometry:-Tensor:-RaiseLowerIndices) expected 1st argument to be a covariant metric tensor or a contravariant metric tensor . Received: _DG([["tensor", M1, [["cov_bas", "cov_bas"], []]], [[[1, 1], 2*H(zeta, u, v)*Ybar(zeta, u, v)^2], [[1, 2], 2*H(zeta, u, v)*Y(zeta, u, v)*Ybar(zeta, u, v)+2], [[1, 3], 2*H(zeta, u, v)*Ybar(zeta, u, v)], [[1, 4], -2*H(zeta, u, v)*Ybar(zeta, u, v)^2*Y(zeta, u, v)], [[2, 1], 2*H(zeta, u, v)*Y(zeta, u, v)*Ybar(zeta, u, v)], [[2, 2], 2*H(zeta, u, v)*Y(zeta, u, v)^2], [[2, 3], 2*H(zeta, u, v)*Y(zeta, u, v)], [[2, 4], -2*H(zeta, u, v)*Y(zeta, u, v)^2*Ybar(zeta, u, v)], [[3, 1], 2*H(zeta, u, v)...

  
M1 > 

``

 

Download Equation_2.16_using_DiffernetialGeometry.mw

 

I appreciate the help.
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